What is (-2+sqrt(-9))^2 ?

The solution to (-2+sqrt(-9))^2 is -5-12i

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simplify (-2+sqrt(-9))^2

simplify

(- 2 + - 9)^{2}

- 5 - 12 i

Solution steps

(- 2 + - 9)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(- 2 + - 9)^{2} = (- 2)^{2} + 2 (- 2) - 9 + (- 9)^{2}

= (- 2)^{2} + 2 (- 2) - 9 + (- 9)^{2}

(- 2)^{2} + 2 (- 2) - 9 + (- 9)^{2} = - 12 i - 5

= - 12 i - 5

Rewrite in standard complex form:

- 5 - 12 i

= - 5 - 12 i

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